Math Problem Statement
Graph the line y = -x - 5
Solution
The equation provided in the image is:
This is a linear equation in slope-intercept form, , where:
- is the slope of the line.
- is the y-intercept, the point where the line crosses the y-axis.
To graph this line:
- Start at the y-intercept: The line crosses the y-axis at .
- Use the slope: The slope is , which means for every unit you move to the right along the x-axis, move down by 1 unit on the y-axis. This gives the direction of the line.
- Plot another point: From , move right by 1 and down by 1 to find another point .
- Draw the line: Once you have two points, you can draw a straight line through them, extending in both directions.
Would you like a detailed graph or any further explanations?
Related questions:
- What is the slope of the line, and how does it affect the direction of the line?
- How do you determine the y-intercept from a linear equation?
- Can we express this equation in another form, such as point-slope form?
- What happens if we change the slope to a positive value?
- How would the graph change if the constant was replaced with a different number?
Tip: To graph any linear equation quickly, always identify the slope and y-intercept first. These give you the key points to plot the line.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Graphing
Formulas
Slope-intercept form y = mx + b
Theorems
Slope of a Line
Y-intercept
Suitable Grade Level
Grades 7-9